Abstract

Null energy condition plays a crucial role in holographic renormalization group flow, leading to the
holographic c-theorem. Unfortunately, the null energy condition is quantum mechanically violated.
Even the averaged version can be violated. We discuss how the anomalous violation of the null
energy condition affects the holographic renormalization group flow in (1 + 3)-dimensional bulk gravity.
We show that despite the violation of the null energy condition, a suitably modified holographic c-function
with a peculiar log correction is still monotonically decreasing in so far as we add the
counterterm that removes a ghost mode of gravity.